(plate_simulation_match)=

# Plate Matching

The plate matching algorithm searches through a library of pre-computed
plate simulations to identify the best-fit conductor geometry for
observed electromagnetic data at query locations. The matching process
involves spatial and temporal interpolation, data normalization, and
correlation-based scoring to rank candidate simulations.

```{figure} images/match_landing.png
---
width: 300pt
align: center
---
```

## Interface

This section describes the parameters controlling the application.

```{figure} images/match_uijson.png
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width: 300pt
align: center
---
Rendered user-interface in Geoscience ANALYST.
```

### Inputs

The algorithm operates on the following inputs:

- **Survey**: A geophysical survey object containing the airborne TEM
  measurements and associated metadata
- **EM data**: Airborne time-domain electromagnetic (TEM) measurements
  from the survey
- **Query Points**: User-defined positions where plate parameters are to
  be estimated
- **Query Max Distance**: Maximum distance from the query points along
  the survey line segments for consideration in the matching process
- **Strike angle**: Optional angle to correct for the strike of the
  conductor relative to the survey line direction
- **Topography**: Object representing the earth-air interface
- **Elevation channel**: Optional channel containing elevation data for
  the topography locations. Mainly used for digital elevation models
  provided on Grid2D objects.
- **Simulation directory**: A directory of pre-computed forward
  simulations representing various plate geometries and conductivities

## Methodology

For each query location, the application identifies the closest survey
line segment, extracts relevant observed data, and compares it against
all simulations in the library using a multi-step matching process. To
accommodate for variable position, time sampling, it is expected that
the simulated library contains sufficient variability in plate
parameters and survey geometries to capture the range of possible
responses.

```{figure} images/match_template.png
---
width: 300pt
align: center
---
Template for the simulated data (black)
and observed data (red) used in the matching process. The radial pattern
centered on the plate allows to tighten sampling around the peak
response, which is critical for accurate matching.
```


The following sections describe the key steps of the matching algorithm.

### Spatial Interpolation

The application performs spatial interpolation to align simulation data
with observation points:

1.  **Local coordinate transformation**: The application identifies the
    survey line segment nearest to each query location. It transforms
    both the observed and simulated receiver locations into a local
    polar coordinate system (distance, azimuth, height) centered on the
    line segment.
2.  **Strike angle correction**: If strike angles are provided, the
    application rotates the coordinate system to align the plate
    orientation with the survey geometry. This accounts for variations
    in conductor strike relative to the flight line direction.
3.  **Inverse distance weighting**: The application constructs a sparse
    interpolation matrix using the 8 nearest simulation receivers for
    each observation point. The weights are computed using inverse
    distance weighting with a power of 2.0 and a minimum distance
    threshold of 0.1 to prevent singularities.

### Temporal Interpolation

Time-domain electromagnetic data requires careful handling of the
temporal sampling:

1.  **Time channel alignment**: The application identifies the overlap
    between simulated and observed time channels. Only time gates within
    the simulated range are considered for matching.
2.  **Interpolation matrix**: For each observation time within the valid
    range, the application constructs a sparse interpolation matrix
    using inverse distance weighting based on the temporal separation
    between channels. This allows for comparison even when simulated and
    observed time samplings differ.

### Data Normalization

To enable robust comparison across different conductivity models and
survey geometries, the application normalizes both observed and
simulated data:

1.  **Symlog transformation**: The application applies a symmetric
    logarithmic transformation to handle the large dynamic range of
    electromagnetic decay curves. The threshold is set at the 5th
    percentile of absolute data values.
2.  **Median centering**: The application subtracts the median value
    from each time channel to remove DC offsets.
3.  **Amplitude scaling**: The application scales each data profile to
    unit maximum absolute value, ensuring that shape matching dominates
    over amplitude matching.

### Orientation Detection

Electromagnetic anomalies are strongly dependent on the direction of
approach relative to the conductor dip. Since simulations are only
computed in the down-dip direction, the application automatically
detects and corrects for orientation reversals:

1.  **Spatial integration**: The application computes the integral of
    positive anomaly values on each half of the survey segment.
2.  **Asymmetry test**: If more than 50% of the time channels show
    stronger anomalies on the left side of the segment, the application
    infers an up-dip approach and reverses the spatial ordering of the
    data.

### Scoring and Ranking

For each simulation file in the library, the application computes a
match score:

1.  **Cross-correlation**: For each time channel, the application
    computes the normalized cross-correlation between observed and
    simulated data. The peak correlation indicates the optimal spatial
    alignment.
2.  **Alignment consistency**: The application records the index of
    maximum correlation for each time channel and computes the median
    alignment position across all channels.
3.  **Residual norm**: The application computes the L2 norm of the
    difference between observed and amplitude-scaled simulated data
    across all time channels and spatial locations. This serves as the
    primary score metric, with lower values indicating better matches.
4.  **Ranking**: The application sorts all simulations by ascending
    score, with the lowest-scoring simulation representing the best
    match.

### Plate Parameter Extraction

Once the best-matching simulation is identified, the application
extracts the plate parameters from the simulation metadata:

1.  **Parameter retrieval**: The application reads the conductor
    geometry (strike length, dip length, width, dip angle, conductivity)
    from the ui.json metadata stored in the simulation file.
2.  **Spatial positioning**: The application positions the plate at the
    centroid of the matched survey segment, adjusted vertically by the
    overburden thickness.
3.  **Orientation correction**: The application applies strike angle
    corrections based on the local line azimuth and any user-specified
    strike angle offsets.
4.  **Plate creation**: The application creates a new `MaxwellPlate`
    object in the output workspace with the extracted geometry and
    stores the full model parameters in the plate metadata.

### Parallel Processing

The matching algorithm leverages parallel processing to accelerate the
comparison of large simulation libraries:

1.  **File batching**: The application divides the simulation library
    into batches, with approximately 10 batches per worker process.
2.  **Distributed scoring**: Each batch is submitted to a Dask worker
    for independent scoring. Workers compute spatial and temporal
    interpolations, normalize data, and calculate correlation scores
    without inter-process communication.
3.  **Result aggregation**: The main process collects scores from all
    workers and performs the final ranking to identify the best match
    for each query location.

This parallel architecture allows efficient processing of libraries
containing hundreds to thousands of pre-computed simulations.